Verification of K-ω SST Turbulence Model for Supersonic Internal Flows

In this work, we try to find the best setting of Computational Fluid Dynamic solver available for the problems in the field of supersonic internal flows. We used the supersonic air-toair ejector to represent the typical problem in focus. There are multiple oblique shock waves, shear layers, boundary layers and normal shock interacting in the supersonic ejector making this device typical in field of supersonic inner flows. Modeling of shocks in general is demanding on the physical model of fluid, because ordinary conservation equation does not conform to real conditions in the near-shock region as found in many works. From these reasons, we decided to take special care about solver setting in this article by means of experimental approach of color Schlieren pictures and pneumatic measurement. Fast pressure transducers were used to measure unsteady static pressure in regimes with normal shock in mixing chamber. Physical behavior of ejector in several regimes is discussed. Best choice of eddy-viscosity setting is discussed on the theoretical base. The final verification of the k-ω SST is done on the base of comparison between experiment and numerical results.

Authors:

• J. Kolář
• V. Dvořák

Keywords:

• CFD simulations
• color Schlieren
• k-ω SST
• supersonic flows
• shock waves.

References:

[1] Breitkopf, P. and Coelho, R. F. Multidisciplinary design optimization in
computational mechanics: Wiley-ISTE, 2010. ISBN-10 1848211384.
[2] Hynek, J. Genetic algorithms and genetic programing (in Czech).
Prague : Grada Publishing ,a. s., 2008. ISBN 978-80-247-2695-3.
[3] Dvoř├ík, V. and Kol├íř, J. Shape optimization of supersonic ejectors with
several primary nozzles. Lisboa, Portugal : In the 2nd International
Conference on Engineering Optimization, 6.-9. september 2010. ISBN
978-989-96264-3-0.
[4] Dvoř├ík, V. Shape optimization of supersonic ejector for supersonic
wind tunnel. s.l. : In.: Applied and Computational Mechanics, 2010. pp.
15-24. ISSN 1802-680X.
[5] Kol├íř, J. and ┼áafař├¡k, P. Interaction of oblique shock wave with shear
layer. Plzeň : In Proceedings of the International Conference XXVII:
Meeting of Departments of Fluid Mechanics and Thermomechanics,
2008. pp. 163-170. ISBN 978-80-7043-666-0.
[6] Moeckel, W. E. Interaction of oblique shock waves with regions of
variable pressure, entropy and energy. Washington : NACA, 1952. TN
2725.
[7] Shapiro, A. H. The dynamics and thermodynamics of compressible
fluid flow. New York : The Ronald Press Company, 1953. ISBN
0826080758.
8] Versteeg, H. K. and Malalasekera, W. An Introduction to
Computational fluid dynamics, The Finite Volume Method: Pearson
Education Limited 2007, ISBN 978-0-13-127498-3.
[9] Wilcox, D. Reassessment of the scale determining equation for
advanced turbulent models. 1988. AIAA J. 26 (11),1299-1310.
[10] Menter, F. R. Two-equations Eddy-viscosity turbulence models for
engineering applications. 1994. AIAA J. 32(8), 1598-1605.
[11] Inc., Fluent. Fluent user documentation. Lebanon : s.n., 2006.
from the biography.